Orthogonal differential vector signaling

ABSTRACT

Using a transformation based at least in part on a non-simple orthogonal or unitary matrix, data may be transmitted over a data bus in a manner that is resilient to one or more types of signal noise, that does not require a common reference at the transmission and acquisition points, and/or that has a pin-efficiency that is greater than 50% and may approach that of single-ended signaling. Such transformations may be implemented in hardware in an efficient manner. Hybrid transformers that apply such transformations to selected subsets of signals to be transmitted may be used to adapt to various signal set sizes and/or transmission environment properties including noise and physical space requirements of given transmission environments.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/511,911, filed Jul. 15, 2019, entitled “Orthogonal DifferentialVector Signaling”, which is a continuation of U.S. application Ser. No.15/818,698, filed Nov. 20, 2017, now U.S. Pat. No. 10,355,756, grantedJul. 16, 2019, entitled “Orthogonal Differential Vector Signaling”,which is a continuation of U.S. application Ser. No. 15/070,909, filedMar. 15, 2016, now U.S. Pat. No. 9,825,677, granted Nov. 21, 2017,entitled “Orthogonal Differential Vector Signaling”, which is acontinuation of U.S. application Ser. No. 12/784,414, filed May 20,2010, now U.S. Pat. No. 9,288,089, granted Mar. 15, 2016, entitled“Orthogonal Differential Vector Signaling”, which claims the benefit ofU.S. Provisional Application No. 61/330,107, filed Apr. 30, 2010,entitled “Orthogonal Differential Vector Signaling”, all of which arehereby incorporated herein by reference in their entirety for allpurposes.

FIELD OF THE INVENTION

The present invention relates to communications in general and inparticular to transmission of signals capable of conveying information.

BACKGROUND OF THE INVENTION

Transmission of digital information on a physical device such as onwires on a computer chip, through optical cables, through twisted paircopper wires, or through cables such as the High-Definition MultimediaInterface (HDMI), and other such physical, tangible and/ornon-transitory transmission media, has been the subject of muchinvestigation. Each piece of the information to be transmitted may beassociated with a continuous time waveform in such a way that differentpieces of information are distinguishable from one another by means oftheir corresponding waveform. For example, where information istransmitted on wires using physical voltages, the pieces of informationcould correspond to the possible values 0 or 1 of a bit, and a 0 couldcorrespond to a voltage of +V with respect to fixed reference voltage,whereas a 1 could correspond to a voltage of −V with respect to the samereference voltage. Where higher modulation is used, the pieces ofinformation could correspond to all possible combinations of a largernumber of bits, and each such group of bits could correspond to adifferent phase of the waveform, or to a different amplitude, or to adifferent frequency. Information may be encoded into a waveform byaltering one or more of its properties. This waveform may be convertedinto a physical, tangible and/or non-transitory embodiment that can becarried by the transmission medium. The process of varying one or moreproperties of a waveform with respect to a baseline modulating signal isherein called the process of modulation. The act of transmitting theinformation using a modulated signal is herein referred to as signaling.

One of the more commonly used methods for transmitting signals overwires is the single-ended signaling method. Where information istransmitted by either applying different voltage levels (voltage mode)on the wire with respect to a reference or sending a current (currentmode) with different strengths into the wire. When using voltages, onewire carries a varying voltage that represents the signal while theother wire is connected to a reference voltage which is usually theground. When using currents, the common return path of the current isusually ground. Hence, in a single-ended signaling method each signalsource is connected to the data acquisition interface using one signalpath. At the data acquisition interface, often voltages are measured,either, directly or by terminating the wire by means of a load to areference. The result of the measurement is proportional to thedifference between the signal and the reference, often “ground” or“earth”, at the acquisition point. The method relies on the signalsource reference to be the same as the data acquisition point'sreference. However, in reality they can be different for a variety ofphysical reasons. This is especially problematic when signals have totraverse longer distances (for example in twisted pair copper wires), orwhen the frequencies of the signals are very high (for example in highthroughput on-chip communication). Using ground as a reference andconnecting the grounds on both ends can drive large currents known asground loops, which can lead to significant errors when usingsingle-ended inputs. Furthermore, it is not always possible to have acommon electrical reference at both sides of the wires. This can be thecase in optical communications. Moreover, single-ended inputs can besusceptible to noise (i.e., unwanted signal contaminations). Forexample, such noise can be added because electrical signal wires act asaerials, and hence pick up environmental electrical activity.Single-ended signaling methods do not always provide sufficientprotection against these sources of noise, especially for high speedcommunications.

To combat these problems, a different form of signaling calleddifferential signaling is used. In conventional differential signaling,information is transmitted using two complementary signals sent on twoseparate wires, for example, in the form of a voltage difference betweenthe wires or current strength and direction in the wires. The outputsignal is then the difference between these two complementary signals.The technique can be used for both analog signaling, for example in someaudio systems, and in digital signaling. Examples include, but are notlimited to standards such as the RS-422, RS-485, the twisted-pairEthernet, the Peripheral Component Interconnect (PCI) Express, theUniversal Serial Bus (USB), serial ATA, Transition MinimizedDifferential Signaling (TMDS) used in DVI and HDMI cables, or theFireWire interface. While sending complementary signals on the two wiresof a differential input is advantageous in some applications, it is notstrictly required. Instead, it is possible to send the information onthe second wire in such a way that the difference in voltage between thesecond and the first wire is +V or −V for some fixed voltage V. At theacquisition point, the receiving device reads the difference between thetwo signals. Since the receiver ignores the wires' voltages with respectto ground, small changes in ground potential between transmitter andreceiver do not affect the receiver's ability to detect the signal. Oneof the main advantages of differential signaling is its resistance to“common-mode noise.” This is noise that affects both wires in the systemin the same way (for example through interference caused by nearbywires). Furthermore, compared to single-ended signaling, the signalswing at the receiver is typically larger which can result in betternoise performance.

In many practical scenarios, communication takes place by sending morethan one bit of information a time. For example, in a 32-bit bus system,32 bits of binary information may be sent simultaneously. In such cases,multiple single-ended, or differential, signaling paths are used inparallel, one for each bit. A disadvantage of conventional differentialsignaling in these practical scenarios is the large number of wiresneeded: to each bit there are two wires associated. The ratio betweenthe number of bits and the number of wires used to transmit these bitsis herein called the pin-efficiency of the system. This number is 1.0(or 100%) for single-ended signaling, whereas it is 0.5 (or 50%) fordifferential signaling. In many communication scenarios, this makes theuse of differential signaling less desirable. To combat this problem, insome cases the signals are serialized and sent over only one, or only afew pairs of differential signal paths. However, this method has thedisadvantage of requiring the transmission to take place at a higherfrequency in order to maintain a given throughput. However, transmissionat higher frequency requires more energy both in order to realize thehigher frequency of operation, and to combat noise associated with thismode of operation.

What is needed is a signaling method that, at least, retains theresilience of differential signaling against various modes of noise, andhas a pin-efficiency that can approach that of single-ended signaling.Embodiments of the invention are directed toward solving these and otherproblems individually and collectively.

BRIEF SUMMARY OF THE INVENTION

Using a transformation based at least in part on a non-simple orthogonalor unitary matrix, data may be transmitted over a data bus in a mannerthat is resilient to one or more types of signal noise, that does notrequire a common reference at the transmission and acquisition points,and/or that has a pin-efficiency that is greater than 50% and mayapproach that of single-ended signaling. Such transformations may beimplemented in hardware in an efficient manner. Hybrid transformers thatapply such transformations to selected subsets of signals to betransmitted may be used to adapt to various signal set sizes and/ortransmission environment properties including noise and physical spacerequirements of given transmission environments.

This Brief Summary of the Invention is provided to introduce a selectionof concepts in a simplified form that are further described below in theDetailed Description of the Invention. This Brief Summary of theInvention is not intended to identify key or essential features of theclaimed subject matter, nor is it intended to be used as an aid indetermining the scope of the claimed subject matter. Other objectsand/or advantages of the present invention will be apparent to one ofordinary skill in the art upon review of the Detailed Description of theInvention and the included figures.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments in accordance with the present disclosure will bedescribed with reference to the drawings, in which:

FIG. 1 is a schematic diagram depicting aspects of an examplecommunication in accordance with at least one embodiment of theinvention;

FIG. 2 is a schematic diagram depicting aspects of an exampletransformer in accordance with at least one embodiment of the invention;

FIG. 3 is a schematic diagram depicting aspects of example componentsfacilitating single-ended signaling;

FIG. 4 is a schematic diagram depicting aspects of example componentsfacilitating conventional differential signaling;

FIG. 5 is a schematic diagram depicting aspects of an examplecommunication bus in accordance with at least one embodiment of theinvention;

FIG. 6 is a schematic diagram depicting aspects of an exampletransformer in accordance with at least one embodiment of the invention;

FIG. 7 is a schematic diagram depicting aspects of an exampledetransformer in accordance with at least one embodiment of theinvention;

FIG. 8 is a schematic diagram depicting aspects of an example decoder inaccordance with at least one embodiment of the invention;

FIG. 9 is a representation of a Hadamard matrix of size 12 in accordancewith at least one embodiment of the invention;

FIG. 10 is a schematic diagram depicting aspects of an example encoderand/or decoder circuit in accordance with at least one embodiment of theinvention;

FIG. 11a is a schematic diagram depicting aspects of another exampleencoder and/or decoder in accordance with at least one embodiment of theinvention;

FIG. 11b is a schematic diagram depicting aspects of yet another exampleencoder and/or decoder in accordance with at least one embodiment of theinvention;

FIG. 11c is a schematic diagram depicting aspects of an exampleforwarder in accordance with at least one embodiment of the invention;

FIG. 11d is a schematic diagram depicting aspects of an example specialsubtractor in accordance with at least one embodiment of the invention;

FIG. 11e is a schematic diagram depicting aspects of still anotherexample encoder and/or decoder in accordance with at least oneembodiment of the invention;

FIG. 11f is a schematic diagram depicting aspects of a further exampleencoder and/or decoder in accordance with at least one embodiment of theinvention;

FIG. 12a is a schematic diagram depicting aspects of another exampletransformer in accordance with at least one embodiment of the invention;

FIG. 12b is a schematic diagram depicting aspects of another exampledetransformer in accordance with at least one embodiment of theinvention;

FIG. 13 is a schematic diagram depicting aspects of an example balancerin accordance with at least one embodiment of the invention;

FIG. 14a is a schematic diagram depicting aspects of an example hybridtransformer in accordance with at least one embodiment of the invention;

FIG. 14b is a schematic diagram depicting aspects of an example hybriddetransformer in accordance with at least one embodiment of theinvention;

FIG. 15a is a schematic diagram depicting aspects of another examplehybrid transformer in accordance with at least one embodiment of theinvention;

FIG. 15b is a schematic diagram depicting aspects of another examplehybrid detransformer in accordance with at least one embodiment of theinvention;

FIG. 16 is a schematic diagram depicting aspects of a conventional DSLconfiguration in accordance with at least one embodiment of theinvention;

FIG. 17 is a schematic diagram depicting aspects of an enhanced DSLconfiguration in accordance with at least one embodiment of theinvention; and

FIG. 18 is a flowchart depicting example steps for orthogonaldifferential vector signaling in accordance with at least one embodimentof the invention.

Same numbers are used throughout the disclosure and figures to referencelike components and features.

DETAILED DESCRIPTION OF THE INVENTION

The System Setting

FIG. 1 illustrates an example communication environment 100 includingtwo devices 102, 104 capable of communication connected by a physicalcommunication bus 120. The communication between the two devices 102,104 takes place on the bus 120. The bus 120 is an example of a medium onwhich signal transmission can take place. The information to betransmitted may be stored in an information storage medium 101, or itmay be available substantially concurrently with the transmission. In atleast one embodiment, the information may be present as a sequence ofbits, but each embodiment is not so limited. In at least one embodimentthe bits are represented by a signal. A common signal to representinformation in digital electronics is a non-return-to-zero (NRZ) signal.The bits are encoded in the amplitude of a square waveform where forexample an amplitude of V represents a logical 0 and an amplitude of 0represents a logical 1. More complicated signals to represent theinformation are possible also. An example is an Orthogonal FrequencyDivision Modulated (OFDM) waveform that is generated by a digitalsubscriber line (DSL) modem. These signals often correspond to physicalquantities such as a voltage levels or currents in a circuit. However,this is not necessary. For example, a signal may be defined by thecontent of a storage medium (e.g., memory) of an electronic component.In applications where bits may be represented in a non-physical form,FIG. 1 can be augmented to have a converter between units 101 and 110whose task is to transform the bits into a physical form. As can be seenby those of skill in the art, the methods disclosed in this applicationalso apply when the atomic parts of the information are not bits, butbelong to a larger alphabet, wherein each alphabet element cancorrespond to one or more properties of a signal.

The information in the form of bits or a signal representing theinformation may be input into a transformer 110. A task of thetransformer 110 is to transform the information in such a way that itcan be transmitted via the signal bus 120. For example, transformer 110could be generating a sequence of waveforms corresponding to theindividual bits of the information in the information storage medium101. An example of such a waveform is non-return-to-zero (NRZ) signalingwhere a logical 0 and a logical 1 are represented by a signal level thatis equal to a or −a over a time interval or cycle of T seconds which insome embodiments of the present invention can be a voltage difference toa given reference. Another example is an optical modulator whichtransforms a 0 or a 1 into light of wavelengths λ₀ and λ₁ or modulatesthe intensity of the generated light beam according to the information.Other types of modulation can also be applied to the present disclosure,for example, modulation by frequency, or by signal phase. Thetransformer 110 can include signal amplification, signal filteringand/or other suitable signal processing functions devised to prepare thesignal for a transport medium of the bus 120. In addition to this, thetask of the transformer may include creating a different set of signalsfrom which the original signals can be recovered, and which areresistant to various types of noise on the bus 120. Example operationsof the transformer 110 in accordance with at least one embodiment of theinvention will be described in greater detail below.

Once the signal input into the transformer 110 is transformed, it may betransmitted on the bus 120. The bus 120 may include one or more signalpaths including one or more physical media capable of transporting thetransformed signal set from one end of the bus 120 to the other end ofthe bus 120. In at least one embodiment of the invention, the ends ofthe bus 120 are separated by physical distance. Each one of these signalpaths and/or physical media (at times referred to below as “wires”) maybe capable of transmitting one or more bits of information at a time.The signals transported on the bus 120 may be subjected to noise whichcauses degradation or corruption of said signals. Among the many sourcesof noise, we mention four types: (a) the common-mode noise which isnoise and interference that is common to the wires in the signal path;where the signal path is located on a chip and has the task oftransmitting information from one part of the chip (for example memory)to another part (for example the CPU) such noise could be caused by thepower-supply, crosstalk, electromagnetic interference (EMI), or othertypes of interference; (b) Independent noise, which corrupts the signalsof each wire independently; (c) Simultaneous switching output (SSO)noise which appears when the total power consumption of the circuits inthe signal path is not constant, thus leading to additional noisecorrupting the signals on the wires; and (d) Reference noise, whichappears when the base references with respect to which the signals aredefined are not the same at the point of origin and the point ofacquisition of the signals; one of the many scenarios in which suchnoise is encountered is when the signals transmitted on the wires arevoltages measured with respect to a reference at the point of origin ofthe signals, and need to be measured with respect to the same referenceat the point of acquisition. Where the signal paths are long, forexample, or where the points of origin and acquisition of the signalsare in two different environments, the reference noise can be quitesubstantial. Furthermore, component tolerances are also a common causeof difference of references at both ends of the signal bus.

Another property of the bus 120 is that of the pin-efficiency. For thepurposes of this disclosure, the pin-efficiency of the signal path isdefined as the ratio between the number of wires in the signal path, andthe number of signals that are simultaneously transmitted. All otheraspects being equal, a system that supports a higher pin-efficiency istypically preferred over one with a lower pin-efficiency. Once thesignal is transmitted by the bus 120, it may enter a detransformer 130.The task of the detransformer 130 includes reconstructing the originalinformation in the information storage medium 101 and/or the signalrepresenting this information. For example, when the information fromthe information storage medium 101 is represented by an NRZ signal, theoutput of the detransformer 130 may be an NRZ signal. In at least oneembodiment of the invention, the communication devices 102, 104containing the transformer 110 and the detransformer 130 are physicallycoupled to the bus 120 by physical bus interfaces 106, 108,respectively. Examples of the physical bus interfaces 106, 108 includepins of a computer chip, optical fiber interfaces, and copper wireinterfaces in accordance with any suitable communication standard. Oncethe signals leave the detransformer 130, they may be transported to oneor more further units in the communication path for further processing.Such further units could include another bus, or they could include anyother part of the communication path in need of the information (forexample a memory unit which stores the information digitally or a DSLmodem that will process the signal). The example devices 102, 104 may becomponents of larger devices not shown in FIG. 1. For descriptiveclarity, arrows between some components 101, 110, 120, 130 in FIG. 1show information and/or signals being transmitted in one direction.However, each embodiment of the invention is not so limited. Forexample, communication between the devices 102, 104 may bebidirectional.

The operation of the example transformer 110 is further described withreference to FIG. 2. In this figure a number, k, of signals denotedS[0], . . . , S[k−1] enter the transformer. These signals are arepresentation of the information in the information storage medium 101(FIG. 1). The transformer may include three units: the balancer 210, theencoder 220, and the drivers 230. Signals S[0], S[k−1] may enter thebalancer 210 first. A task of the balancer 210 is to convert theinformation in the information storage medium 101, or the signalrepresenting this information, to a form that can be handled by theencoder 220. For example, for an NRZ signal, the signal levels can beadjusted before entering the encoder 220. If the signals entering thebalancer 210 correspond to bits, then they are mapped to real numbers. Alogical 0 can for example be represented by a 1 and a logical 1 by a −1.These signals are then forwarded to the encoder. The encoder producesfrom the output of the balancer n signals. These signals can then bepassed to a signal path driver 230 which can amplify the signal andapply additional filtering. Furthermore, the signal path driverstransmit the signal denoted B[0], . . . , B[n−1] on bus 120. When themedium does not carry electrical signals, the signal driver can alsoinclude a transducer transforming the signals to another physicalquantity, for example light. In a system employing a transformer withthese parameters, the pin-efficiency is equal to k/n, since k bits arebeing transmitted with the help of n waveforms on the bus 120.

FIG. 3 depicts aspects of example components facilitating single-endedsignaling. Units 310 may be understood as performing a balancingfunction corresponding to the balancer 210 (FIG. 2). These units 310create for every incoming signal another signal that can differ withrespect to the reference 320. Where these signals correspond tovoltages, these units put on their outgoing wires one of two possiblevoltages wherein these voltages depend on the reference 320. Forexample, these units could put a voltage of V or V+a on these wireswhere V is the voltage of the reference point and a is a predeterminedvoltage. These voltages are then forwarded directly to the bus 120, sothat no components corresponding to the encoder 220 are necessary inthis case. The pin-efficiency of single-ended signaling is 1.0 or 100%.However, single-ended signaling suffers from a plurality of noise types,as described earlier. A common approach to alleviate these problems isto increase the value of a thereby increasing the total energyconsumption. However, in applications this may lead to otherdisadvantageous effects (such as battery drain, or induction of noise onother devices).

FIG. 4 depicts aspects of example components facilitating conventionaldifferential signaling. In this example, the input signals aredesignated s[0], . . . , s[3]. No components corresponding to thebalancer 210 (FIG. 2) are necessary in this example. Units 410 feeds twowires for each incoming signal s[0], . . . , s[3]. The amplitude of thesignal put on the first wire is V+s[i] and that of the signal put on thesecond wire V−s[i] for 1=0,1, . . . ,3. The amplitude of the signals ischosen so that the difference in amplitude between the first and secondwire is 2s[i]. The value of Vis typically unimportant, and can be chosento be 0, since the information is encoded by the difference of theamplitudes of the signals put on the two wires. Units 410 may beunderstood as performing an encoding function corresponding to theencoder 220.

Differential signaling is resistant to some of the noise scenariosdiscussed above: it is resistant to common mode noise since theinformation is encoded as the difference of voltages of two wires.Differential signaling provides a better resistance to bus noise thansingle-ended signaling. One of the reasons is that the swing inamplitude is twice as large as in single-ended signaling. As will beapparent to one of skill in the art, in single-ended signaling sometransmission power may be wasted in a DC value of the transmittedsignal. Differential signaling does not introduce SSO noise in case ofchip-to-chip communication of NRZ-like signals. Finally, it is alsoresistant to reference noise because no external reference is requiredto reconstruct the original signals. However, differential signaling hasthat disadvantage that its pin-efficiency is 0.5 or 50%.

FIG. 5 depicts aspects of an example communication bus 500 in accordancewith at least one embodiment of the invention. The communication bus 500is an example of the bus 120 (FIG. 1). The bus 500 includes a pluralityof signal paths such as the signal path 510. Each signal path mayinclude transmission media such as wires (e.g., metallic wires) on whichinformation is transmitted in the form of electrical voltages orcurrents. In chip-to-chip communications these wires may be on-chipinterconnects, PCB traces or strip lines. Yet another application is DSLcommunications where each bus wire may correspond to one wire of atwisted pair copper line typically used in DSL communications. A similarapplication is unshielded twisted pair (UTP) Ethernet communicationswhere again a wire of the bus 500 may correspond to one of the wires ina twisted pair. For communication between devices such as camera's,laptops, TVs, etc, the bus 500 may be in accordance with any suitableconventional communication standard and/or specification. In otherembodiments, the signal paths can be optical cables transmitting opticalsignals in form of light. In yet other embodiments, the signal paths canbe media suited to the transmission of signals.

In at least one embodiment of the invention, each signal is physical,tangible and/or non-transitory in time. In at least one embodiment ofthe invention, a physical signal is a signal that is tangibly embodiedin a tangible and/or physical transmission media. In at least oneembodiment of the invention, transformation of signals includes physicaltransformation of physical signals as part of a physical mechanism. Inat least one embodiment of the invention, signals are tangible aspectsof an apparatus. In at least one embodiment of the invention, signalsare transformed by a mechanism in accordance with physical principleswell known to those of skill in the art.

Example of Orthogonal Differential Vector Signaling

The description now turns to an example of orthogonal differentialvector signaling with reference to FIG. 6. FIG. 6 depicts aspects of anexample transformer 600 in accordance with at least one embodiment ofthe invention. The transformer 600 has a pin-efficiency of 0.75 or 75%,and has input including three signals b[0], b[1] and b[2]. These signalsrepresent the information in the information storage medium 101. Thebalancer 210 creates four signals s[0], s[1], s[2] and s[3] from theincoming three signals b[0], b[1] and b[2]. The first signal s[0] is setto V and the other signals s[1], s[2] and s[3] are set with respect tothis first signal s[0]. This task is done by the units 610 which sets[i] to b[i−1]−V for i=1,2,3. Depending on the application V can be setto 0 or some other suitable value. In chip-to-chip communication b[0],b[1] and b[2] may be single-ended NRZ signals with associated signallevels of a and 0. In this case V may be set to a/2 to remove the meanvalue of the single-ended NRZ signal. The four generated signals s[0],s[1], s[2] and s[3] may then enter the encoder 220. The encoder 220 mayinclude various components such as adders such as adder 630, subtractorssuch as subtractor 631, multipliers such as multiplier 640, and pathsconnecting these components such as paths 621, 622, 623, 635 and 636. Inat least one embodiment, the multipliers are incorporated into thedrivers 230. A task of the adders is to add incoming values and passthem on the outgoing paths. A task of the subtractors is to subtract thelower incoming value from the upper one and pass it on the outgoingpaths. A task of the multipliers is to multiply the incoming value by asuitable factor (e.g., 0.5 in this case) and to pass it along theoutgoing path. For example, the adder 630 computes the addition of thevalues of its incoming paths 635 and 622 which is s[0]+s[1] and passesit on the paths 635 and 636. Similarly, the subtractor 631 subtracts thevalue of its lower incoming path 621, namely s[1], from the value of itsupper incoming path, namely s[0], and passes on the result s[0]−s[1]along its outgoing paths. The output of the encoder 220 is four valuesW[1], . . . , W[4].

For example, if s[0]=0, the output of the encoder 220 has the followingrelationship to the encoder input:

W[1]=(s[1]+s[2]+s[3])/2

W[2]=(−s[1]+s[2]−s[3])/2

W[3]=(s[1]−s[2]−s[3])/2

W[4]=(−s[1]−s[2]+s[3])/2

The total energy of these values, defined as the square root of the sumof the squares of these numbers, is the same as the total energy of theoriginal values 0, s[1], s[2], s[3], namely the square root ofs[1]²+s[2]²+s[3]². In chip-to-chip communications where signals s[1],s[2] and s[3] are balanced NRZ signals, this means that the new signalsW[1], . . . ,W[4] sent on the bus 120 may reduce SSO noise. In addition,as will be seen below, in at least one embodiment of the invention,these signals W[1], . . . ,W[4] are resistant to common mode noise,moderate amounts of independent noise, as well as reference noise.

The Detransformer

Aspects of an example detransformer 130 (FIG. 1) in accordance with atleast one embodiment of the invention are depicted in FIG. 7. Theexample detransformer 130 includes a bus receiver 710, a decoder 720 anda detector 730. The signals 705 coming from the bus 130 enter thedetransformer through bus receiver 710. The bus receiver 710 measuresthe relevant quantities at the bus. If required for the actualmeasurement, the bus receiver 710 could perform amplification andfiltering also. The bus receiver 710 sends signals to the decoder 720.The decoder performs the inverse tasks of the encoder 220, as describedin more detail below.

A task of the detector 730 is to reproduce the original informationstored in the information storage medium 101 (FIG. 1) from the signalsobtained from the decoder 720. The signals delivered by the decoder 720can be corrupted by several sources of noise. The amount of noise thatis tolerable by the detector depends on the applications, on theenvironment, and on the energy spent on the signals, and on theresources of the detector 720. Typically, but not necessarily, the noiseon the incoming signals may be modeled by a Gaussian variable of a givenvariance, wherein bigger variances correspond to a larger amount ofnoise, and smaller variances correspond to smaller amounts of noise.Based on assumptions on the noise, the detector 720 may attempt toreconstruct the original information in 101 or a physical representationof this information. One of skill in the art will recognize that severaldetection techniques known from communication theory can be applied.Furthermore, it is possible to change the order of and/or to integratedecoding and detection. Depending on the exact implementation of thedetector 730 this may result in a performance degradation (or not).

FIG. 8 depicts aspects of an example decoder 720 suitable for decodingsignals generated by the encoder 220 (FIG. 2) as described above withreference to FIG. 6, in which three signals b[0], b[1] and b[2] wereencoded in accordance with at least one embodiment of the invention fortransmission over four wires. The decoder 720 corresponds to the encoder220 of FIG. 6. Differences between the encoder 220 and decoder 720include that the first output of this unit may be discarded in thedecoder 720. This is the case if the first input s[0] of encoder 220 inFIG. 6 was set to 0. The input to the decoder 720 includes the signalsI[1], . . . , I[4], and the output includes the signals r[1], r[2], r[3]corresponding to signals s[1], s[2], s[3] input to the encoder 220 ofFIG. 6. The dashed signal paths in FIG. 8 indicate that these signalpaths may be discarded in an at least one embodiment of the invention,though this need not be the case. In at least one embodiment of theinvention, it may be an advantage that, for example, where the cost ofmanufacturing different encoding and decoding units is a factor, a usermay choose to use as the decoder 720 a same and/or similar hardware unitas for the encoder 220. The first output r[0] of the decoder unit 720may also be utilized as a noise sensor. This can be used in a feedbackloop to cancel the common-node noise from the wires even before enteringthe bus receiver 710. Other options also exist. For example, instead oftransmitting a 0 on the first wire of the bus, it is possible totransmit a clock signal that can be used for synchronization. Eventhough this clock would be highly disturbed by noise, it could still beused to synchronize.

Matrix Interpretation of the Encoder and the Decoder

The operations of the encoder 220 and the decoder 720 according to thepresent invention can be succinctly described in terms of a class ofmatrices known to those of skill in the art as Hadamard matrices. AHadamard matrix of size n is a square matrix of size n which contains asentries either +1 or −1, and for which any two different rows areorthogonal. A square matrix in which different rows are orthonormal isknown as an orthogonal matrix in the literature. Therefore, a Hadamardmatrix with normalized rows and columns is an orthogonal matrix. In whatfollows, the term “Hadamard matrix” may be read as “Hadamard matrix withnormalized rows and/or columns” unless clearly contradicted by context.

A simple Hadamard matrix of size 2 is the matrix

$H_{2} = {{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}}.}$

A special recursive construction of a Hadamard matrix H₂ ^(n) of size2^(n) is furnished by the Sylvester construction:

$H_{2^{n}} = {{\frac{1}{\sqrt{2}}\begin{bmatrix}H_{2^{n - 1}} & H_{2^{n - 1}} \\H_{2^{n - 1}} & {- H_{2^{n - 1}}}\end{bmatrix}}.}$

Other constructions of Hadamard matrices are also known to specialistsin the field as long as the size of the matrix is divisible by 4. Forexample, a Hadamard matrix of size 12 is given in FIG. 9.

Properties of Hadamard matrices include orthogonality and the fact thatthe multiplication of the matrix with a vector in which all componentsare equal produces a vector which has a nonzero entry in only one of itscoordinate positions. As far as efficient implementation is concerned, athird property that is useful for the implementation of methods inaccordance with at least one embodiment of the invention is efficiencyof the multiplication of the matrix with a given vector. Hadamardmatrices of Sylvester type (“Sylvester Hadamard matrices”) satisfy thesethree requirements and therefore are particularly well suited forimplementing the methods in accordance with at least one embodiment ofthe invention. Moreover, Sylvester Hadamard matrices are symmetric,which means that they are identical to their inverses. As will beapparent to one of skill in the art, this fact has further positiveimplications for hardware realizations of methods in accordance with atleast one embodiment of the invention.

The operation of the example encoder 220 is now succinctly described interms of matrices. The signals leaving the balancer 210 and entering theencoder 220 are for the purposes of this presentation denoted by s[1], .. . , s[k] and H is a Hadamard matrix of size k+1. The signals leavingencoder 220 are then the values v[0], . . . ,v[k] wherein

$\begin{bmatrix}{v\lbrack 0\rbrack} \\{v\lbrack 1\rbrack} \\\vdots \\{v\lbrack k - 1\rbrack} \\{v\lbrack k\rbrack}\end{bmatrix} = {{H\begin{bmatrix}0 \\{s\lbrack 1\rbrack} \\\vdots \\{s\lbrack k - 1\rbrack} \\{s\lbrack k\rbrack}\end{bmatrix}}.}$

Decoder 720 performs the inverse operation. If the signals leaving thebus receiver 710 are denoted I[0], . . . , I[k], then the operation ofdecoder 720 corresponds to the multiplication

$\begin{bmatrix}{r\lbrack 0\rbrack} \\{r\lbrack 1\rbrack} \\\vdots \\{r\lbrack k - 1\rbrack} \\{r\lbrack k\rbrack}\end{bmatrix} = {{H^{- 1}\begin{bmatrix}{I\lbrack 0\rbrack} \\{I\lbrack 1\rbrack} \\\vdots \\{I\left\lbrack {k - 1} \right\rbrack} \\{I\lbrack k\rbrack}\end{bmatrix}}.}$

wherein r[1], . . . , r[k] are the signals that leave decoder 720. Thevalue of r[0] may be chosen to be “irrelevant”, that is, not directlycorresponding to one of the signals s[1], . . . , s[k]. It should benoted that the first value r[0] is chosen to be irrelevant only forillustrative purposes. Which of the values r[i] is irrelevant depends onthe Hadamard matrix chosen. For example, for the Hadamard matrix oforder 12 depicted in FIG. 9, the last entry r[k] would be irrelevant. Ingeneral, where H is a Hadamard matrix in which the row with index jconsists entirely of ones, the corresponding entry r[j] would beirrelevant.

The act of signaling corresponding to the multiplication by a Hadamardmatrix as described above is named Hadamard differential vectorsignaling (a special case of orthogonal differential vector signaling,as described in more detail below).

Sylvester type Hadamard matrices are particularly useful for Hadamarddifferential vector signaling. For example, such matrices areself-inverse, i.e., they are identical to their inverse. This means thatthe encoder 220 and the decoder 720 can be substantially identical. Thiscan be advantageous since no additional development costs are necessaryfor the decoder 720.

Another reason for use of Sylvester type Hadamard matrices is a veryefficient procedure for multiplying such matrices with a vector known asthe Fast Hadamard-Walsh Transform. An example of such a transform isgiven with reference to FIGS. 10 and 11 a for the Sylvester typeHadamard matrices of sizes 4 and 8, respectively. In FIG. 10 the circuit1000 corresponding to H₄ (the Sylvester Hadamard matrix of size 4)includes adders such as the adder 1010, subtractors such as thesubtractor 1020, and multipliers such as the multiplier 1030. Asdescribed above for the encoder 220 with reference to FIG. 6, a task ofthe adder 1010 is to add the values of its incoming signals and passthem on the outgoing signal paths. Similarly, a task of the subtractor1020 is to subtract the value of the lower incoming signal from that ofthe upper incoming signal and pass it along its outgoing paths. Themultiplier 1030 has a task of multiplying the incoming signal by afactor (e.g., 0.5 in this case) and passing it along its outgoing path.The mathematical relationship between the incoming signals a[0], . . . ,a[3] and the outgoing signals b[0], . . . , b[3] can be described by theidentity

$\begin{bmatrix}{b\lbrack 0\rbrack} \\{b\lbrack 1\rbrack} \\{b\lbrack 2\rbrack} \\{b\lbrack 3\rbrack}\end{bmatrix} = {{H_{4}\begin{bmatrix}{a\lbrack 0\rbrack} \\{a\lbrack 1\rbrack} \\{a\lbrack 2\rbrack} \\{a\lbrack 3\rbrack}\end{bmatrix}}.}$

Similarly, the adders such as the adder 1110 and subtractors such as thesubtractor 1120 in FIG. 11a perform the same task as their correspondingcounterparts in FIG. 10. However, multipliers such as the multiplier1130 perform a slightly different task: they multiply the incomingsignal by a factor of 1/√{square root over (8)}. As can be seen, therelationship between the incoming signals a[0], . . . , a[7] and theoutgoing signals b[0], . . . , b[7] is given by the identity

$\begin{bmatrix}{b\lbrack 0\rbrack} \\{b\lbrack 1\rbrack} \\\vdots \\{b\lbrack 6\rbrack} \\{b\lbrack 7\rbrack}\end{bmatrix} = {{H_{8}\begin{bmatrix}{a\lbrack 0\rbrack} \\{a\lbrack 1\rbrack} \\\vdots \\{a\lbrack 6\rbrack} \\{a\lbrack 7\rbrack}\end{bmatrix}}.}$

The operations described in FIGS. 10 and 11 a can be generalized forSylvester type Hadamard matrices of size 2n for any n, as will beapparent to those of skill in the art. Such operations may be understoodas corresponding to a Fast Hadamard-Walsh Transformation (FHWT).

In applications where the implementation of a subtractor unit, such assubtractors 1020 and 1120, is costly or otherwise undesirable, thecomputation of a Hadamard-Walsh Transformation can be changed in such away as to substantially reduce the number of subtractors. The method isbased on binary versions of Hadamard matrices. If in denotes then×n-matrix in which all entries are equal to the number 1, and if Hdenotes an n×n-Hadamard matrix, then the binary version of H is thematrix

T=1/2(H+1_(n))

If a procedure calculates for a given vector x the product Tx, then themethod can be used to also calculate the product Hx, since

H·x=2·T·x−1_(n) ·x

The entries of the vector 1_(n)·x are all equal to the sum of theentries of the vector x. For Sylvester type Hadamard matrices thecorresponding binary matrix has the advantage that its product with avector can be calculated efficiently without using any subtractors. Themethod is exemplified with reference to FIG. 11b-11f . The circuit 1132in FIG. 11b computes the Hadamard-Walsh Transformation of the vector(a[0],a[1],a[2],a[3]) which is equal to the vector(b[0],b[1],b[2],b[3]). It uses forwarder units such as the forwarderunit 1135, special subtractor units such as the special subtractor 1140,adders 1138, and multiplier units such as the multiplier 1145. Theoperation of the forwarder 1135 is explained with reference to FIG. 11c. A task of the forwarder 1135 is to forward the incoming value x alongeach of its one or more outgoing paths. A task of the special subtractor1140 is described with reference to FIG. 11d . The task is to form thevalue 2y-x for incoming values x and y.

Coming back to FIG. 11b , it can be seen that the output of the gates inthe layer denoted 1138 is equal to the vector (a[0]+a[1]+a[2]+a[3],a[0]+a[2], a[0]+a[1], a[0]+a[3]). In other words, it is equal to theproduct

$\begin{bmatrix}{c\lbrack 0\rbrack} \\{c\lbrack 1\rbrack} \\{c\lbrack 2\rbrack} \\{c\lbrack 3\rbrack}\end{bmatrix} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 0 & 1 & 0 \\1 & 1 & 0 & 0 \\1 & 0 & 0 & 1\end{bmatrix} \cdot \begin{bmatrix}{a\lbrack 0\rbrack} \\{a\lbrack 1\rbrack} \\{a\lbrack 2\rbrack} \\{a\lbrack 3\rbrack}\end{bmatrix}}$

The matrix in this multiplication is the binary version of 2·H₄. Thesignals calculated in this layer are processed in the next layer asfollows: the forwarder 1136 forwards the value of the first gate, i.e.,c[0], and the subtractors in the layer 1142 such as subtractor 1140calculate the values 2c[1]−c[0], 2c[2]−c[0], 2c[3]−c[0]. Therefore, thevalue of the output gates in layer 1142 equals (2c[0]−c[0],2c[1]−c[0],2c[2]−c[0],2c[3]−c[0]), which can be seen to be equal to

$2 \cdot H_{4} \cdot \begin{bmatrix}{a\lbrack 0\rbrack} \\{a\lbrack 1\rbrack} \\{a\lbrack 2\rbrack} \\{a\lbrack 3\rbrack}\end{bmatrix}$

The task of the final multipliers is to multiply the incoming signals by0.5.

Another example of the calculation of a FHWT of a vector of length 8 isfurnished by FIGS. 11e and 11f In addition to forwarders andsubtractors, the example in FIG. 11e uses null gates such as the nullgate 1150. The task of the null gates is to forward a null value (e.g.,0) along all outgoing paths. The value of the gates in layer 1152 isequal to the product

$\sqrt{8} \cdot T_{8} \cdot \begin{bmatrix}{a\lbrack 0\rbrack} \\{a\lbrack 1\rbrack} \\\vdots \\{a\lbrack 7\rbrack}\end{bmatrix}$

wherein T₈ is the binary version of the Hadamard matrix H₈. The task ofthe multipliers such as the multiplier 1155 is to multiply the incomingvalues by the quantity 1/√{square root over (8)}. The values (b[0], . .. , b[7]) satisfy the relation

$\begin{bmatrix}{b\lbrack 0\rbrack} \\{b\lbrack 1\rbrack} \\\vdots \\{b\lbrack 6\rbrack} \\{b\lbrack 7\rbrack}\end{bmatrix} = {H_{8}\begin{bmatrix}{a\lbrack 0\rbrack} \\{a\lbrack 1\rbrack} \\\vdots \\{a\lbrack 6\rbrack} \\{a\lbrack 7\rbrack}\end{bmatrix}}$

The operation of the circuit 1160 in FIG. 11e is further simplified withreference to FIG. 11f . The basic difference between these two versionsis that the circuit 1170 in FIG. 11f does not contain any null gates,and is obtained from the circuit 1160 in FIG. 11e by removing the nullgates and all communication paths emanating from them.

In general, if T₂ _(n) , denotes the binary version of the Hadamardmatrix H₂ _(n) and if U₂ _(n) denotes the matrix in which all entries ofT₂ _(n) , are inverted (0 is inverted to a 1, and 1 is inverted to a 0),then we have the recursion

${T_{2^{n + 1}} = {\frac{1}{\sqrt{2}}\begin{bmatrix}T_{2^{n}} & T_{2^{n}} \\T_{2^{n}} & U_{2^{n}}\end{bmatrix}}},{U_{2^{n + 1}} = {\frac{1}{\sqrt{2}}\begin{bmatrix}U_{2^{n}} & U_{2^{n}} \\U_{2^{n}} & T_{2^{n}}\end{bmatrix}}}$

These two recursions can be used to efficiently compute T₂ _(n) , x forany vector x. The examples in FIG. 11b, 11e, 11f may be determined basedon these recursions.

General Operation of Orthogonal Differential Vector Signaling

An example transformer 1201 and an example detransformer 1260 inaccordance with at least one embodiment of the invention are nowdescribed with reference to FIG. 12a and FIG. 12b . The transformer 1201in FIG. 12a makes use of a Hadamard matrix H of size n. The input 1205of the transformer includes n-1 of signals which enter the balancer1210. The output of the balancer 1210 includes n signals which enter theencoder 1220. A task of the encoder 1220 is to perform themultiplication of the Hadamard matrix H with the vector of n signalsleaving the balancer 1210. The output of the encoder 1220 corresponds tothe vector that is formed by multiplying H with the vector of signalsleaving the balancer 1210. The output of the encoder 1220 is fed to thesignal path driver drivers 1225 which possibly perform additionalamplification and/or filtering. Furthermore, the signal path driver mayact as a transducer making the signal suitable for transmission on thebus 120 (FIG. 1).

The detransformer 1260 described in FIG. 12b includes a bus receiver1230, a decoder 1240 and a detector 1250, n signals 1225 coming from thebus 120 (FIG. 1) and possibly corrupted by various types of noise asdescribed above. The bus receiver 1230 may amplify the signal andpossibly apply some filtering and equalization. Thereafter, the signalsare forwarded to decoder 1240. A task of the decoder is to multiply then incoming signals with the inverse H⁻¹ of the matrix H used at thetransformer 1201.

In accordance with at least one embodiment of the invention, thepin-efficiency of communicating utilizing the transformer 1201 and thedetransformer 1260 is (n-1)/n.

Example operation of the balancer 1210 presenting accordance with atleast one embodiment of the invention is described with reference toFIG. 13. The inputs to the balancer 1210 are denoted by a[1], . . . ,a[n-1]. The output of the balancer 1210 includes n signals of which thefirst 1320 is set to a value of V. The balancer uses units such asbalancing unit 1310 to set the other output signals s[1], . . . , s[n-1]to a[i]−V for 1=1,2, . . . , n-1. Where signals are transmitted by meansof difference in amplitude, the task of units 1310 is to read theincoming values, and put an amplitude difference on the outgoing wireswith respect to “additional” wire 1320. Since only differences inamplitude are considered, the value of the signal on this additionalwire can be thought of as zero (0). The output of the balancer is thesignal “0” on wire 1320, and values s[1], . . . , s[n-1] on the otheroutgoing wires. Where the output of the balancer on wire 1320 is 0, thevalues s[1], . . . , s[n-1] can be substantially equal to the values oftheir counterparts a[1], . . . , a[n-1]. It is not necessary that thesignals are transmitted as voltage differences. Other types ofdifferences can work in accordance with at least one embodiment of theinvention.

Properties of Orthogonal Differential Vector Signaling

Orthogonal differential vector signaling in accordance with at least oneembodiment of the invention has a number of pertinent propertiesincluding:

-   -   Resilience to common mode noise: common mode noise as described        above is additive noise of a same magnitude on each signal path        of the bus 120 (FIG. 1). Orthogonal differential vector        signaling is resistant to this type of noise. If the signal        vector (s[0], s[1], . . . , s[n-1]) is sent over the bus 120,        and the signal (s[0]+v, s[1]+v, s[n-1]+v) is received at the        detransformer 130, then the operation of the decoder 1240 (FIG.        12b ) on this vector is equivalent to its multiplication from        the left by the inverse of the Hadamard matrix H. Since the        Hadamard matrix is orthogonal, its inverse is its transposed        matrix, which is again a Hadamard matrix. The output of the        decoder 1240 is then equal to

${H^{- 1}\begin{bmatrix}{{s\lbrack 0\rbrack} + v} \\{{s\lbrack 1\rbrack} + v} \\\vdots \\{{s\left\lbrack {n - 2} \right\rbrack} + v} \\{{s\left\lbrack {n - 1} \right\rbrack} + v}\end{bmatrix}} = {{H^{- 1}\begin{bmatrix}{s\lbrack 0\rbrack} \\{s\lbrack 1\rbrack} \\\vdots \\{s\lbrack n - 2\rbrack} \\{s\lbrack n - 1\rbrack}\end{bmatrix}} + {\begin{bmatrix}* \\0 \\\vdots \\0 \\0\end{bmatrix}.}}$

-   -   wherein we have assumed that the Hadamard matrix H is chosen in        such a way that the irrelevant output of its inverse is the        first one. Accordingly, the common mode noise may affect the        irrelevant output of the decoder 1240, but not the decoding and        later detection of the data.    -   Resilience to independent noise: Since the Hadamard matrix is an        orthogonal matrix, the multiplication of this matrix with a        vector including independent Gaussian noise variables is a        vector of independent Gaussian noise variables of the same noise        level. A detector 1250 can be constructed that operates        independently on the outputs of the decoder 1240 without        incurring a performance loss. This makes detection easy and        suitable for hardware implementation. In some cases detection        may be performed units later in the communication chain. For        these units the encoder 1220 and decoder 1240 described in this        disclosure may be transparent and/or hidden. It may be that,        accordingly, such units do not have to cope with a more complex        noise structure.    -   Resilience to SSO noise: Since the Hadamard matrix is        orthogonal, the total energy of the input signals before        encoding can correspond to the total energy after encoding. This        property makes this signaling resistant to SSO noise.    -   Resilience to Reference noise: Since orthogonal differential        vector signaling need not require a common reference between the        sender and the receiver of the signals, the method can be        resistant to reference noise.    -   Relatively High Pin-efficiency: unlike conventional differential        signaling which can have a pin-efficiency near 50%, the        pin-efficiency of orthogonal differential vector signaling in        accordance with embodiments of the invention may approach the        perfect pin-efficiency of 100%, as it may correspond to (n-1)/n.        For example, where n is 32, the pin-efficiency may be 31/32        which is almost equal to 97%. Where n is 64, the pin-efficiency        may approach 98.5%.

Hybrid Orthogonal Differential Vector Signaling

In certain applications it may be desirable to subdivide the signalingpaths of the bus 120 (FIG. 1) into smaller groups and to performorthogonal differential vector signaling with respect to these smallergroups, rather than with respect to the entire set of signaling paths atone time. For example, it may be the case that the width of the bus 120(e.g., with respect to physical distance) makes the common mode noiseassumption a realistic one only for a relatively small group of adjacentsignal paths. In other applications it is possible that the additionalcost of the encoder 1220 (FIG. 12a ) and the decoder 1240 isproblematic. In such cases a hybrid method in accordance with at leastone embodiment of the invention may be preferable.

An example method of hybrid orthogonal differential vector signaling inaccordance with at least one embodiment of the invention is nowdescribed with reference to FIGS. 14a and 14b . The example transformer1402 in FIG. 14a has 9 incoming signals 1410 and sends 12 signals 1420over the bus 120 (FIG. 1). It therefore has a pin-efficiency of ¾ or75%. The incoming signals 1410 are subdivided into three groups of threesignals each. Each of these three groups is transformed using thetransformer 1201 of FIG. 12a wherein the Hadamard matrix is theSylvester type matrix H₄. Similarly, the incoming wires into an exampledetransformer 1404 in FIG. 14b are grouped into three groups 1430 of 4wires each. Each of these groups is detransformed using detransformer1250 of FIG. 12b wherein the Hadamard matrix is the Sylvester typematrix H₄. As can be appreciated by those of skill in the art, hybridorthogonal differential vector signaling may have a same and/or similarresiliency to noise as orthogonal differential vector signaling.

Hybrid orthogonal differential vector signaling can also be used insituations where there is no Hadamard matrix supporting the number ofincoming wires. In at least one embodiment of the invention, suchsituations are abundant. For example, in many communications scenariosthe number of incoming wires into transformer 110 is a power of thenumber 2, for example 16, 32, 64, 128, or alike. To transform thesesignals it would be necessary to have a Hadamard matrix of size one morethan a power of 2, for example, 17, 33, 65, 129, or alike. However, inat least one embodiment of the invention, Hadamard matrices of thesesizes do not exist. To overcome this problem, a hybrid orthogonaldifferential vector signaling method in accordance with at least oneembodiment of the invention can be used. An example such method is nowdescribed with reference to FIG. 15a and FIG. 15b for the case where thenumber of incoming wires is 32.

The example transformer 1502 in FIG. 15a has 32 incoming wires which aresubdivided into a first group 1510 of 31 wires and another group 1520 ofone wire. The first group 1510 is transformed using transformer 1201 ofFIG. 12a wherein the Hadamard matrix is the Sylvester type matrix H₃₂and the second group is transformed using a transformer that uses theSylvester Hadamard matrix H₂. Correspondingly, there are 34 outgoingwires of which a group 1530 of 32 wires exit the first transformer,whereas a group 1540 of two outgoing wires exit the second transformer.Similarly, the incoming wires into transformer 1504 of FIG. 15b aregrouped into two groups wherein the first group 1550 includes 32 wiresand the second group 1560 includes two wires. The first group isdetransformed using detransformer 1250 of FIG. 12b wherein the Hadamardmatrix is the Sylvester type matrix H₃₂. The second group isdetransformed using detransformer 1250 using the Hadamard matrix H₂. Thepin-efficiency of this hybrid method is 32/34 which is about 94%.

Hybrid signaling can be used for any suitable number of incoming wires.For example, where the number of incoming wires is m, one can findintegers k₁≥k₂≥ . . . ≥k₁>0 such that m=2₁ ^(k)+2₂ ^(k)+ . . . +2 _(t)^(k)−t. Subdividing the incoming wires into groups of sizes 2₁ ^(k)−1,2₂ ^(k), . . . , 2_(t) ^(k)−1 and using Sylvester type Hadamard matrices

H ₂ _(k) ₁ ,H ₂ _(k) ₂ , . . . ,H ₂ _(k) _(t).

will lead to a hybrid differential signaling method with pin-efficiencym/(m+t). For example, when m=24, then we can write

24=2⁴−1+2³−1+2¹−1+2¹−1

and this decomposition describes a hybrid differential vector signalingmethod of pin-efficiency 24/28 which is about 86%.

Multilevel Signaling

In certain applications, the information in the information storagemedium 101 of FIG. 1 may include a sequence of vectors of bits, ratherthan of bits. In this case the signals representing these vectors ofbits may be multilevel encoded. It is readily appreciated by those ofskill in the art that the methods disclosed in this application can beapplied to the case of multilevel signaling as well. For example,vectors corresponding to multilevel signals may be multiplied by aHadamard matrix. The entries of the vector which is multiplied by thismatrix can be any quantities that can be described by real numbers. Inthe case of multilevel signaling, individual entries of the vector cancorrespond to more than two values.

Peak Signal Value

In at least one embodiment of the invention, a further differencebetween orthogonal differential vector signaling and conventionaldifferential signaling is that, in orthogonal differential vectorsignaling, the signals sent on the bus 120 (FIG. 1) may have anexpansion of the number of signal levels. For example, in conventionaldifferential signaling, where signals are differences of voltages withmagnitudes +a or −a, the signals on the bus 120 will all have one ofthese two values. However, where orthogonal differential vectorsignaling with the Hadamard matrix H₄ is used, the largest values on thebus could be twice as large. In general, when a Hadamard matrix H₂ isused, the maximum values on the bus can be a factor of √{square rootover (2 ^(n))} larger. Typically, this is not a problem, because thetotal energy of the signals on the wire is comparable to the totalenergy of the signals entering the transformer 110. However, in certainapplications this may be an inconvenience.

A first solution to this problem is the use of hybrid orthogonaldifferential vector signaling as described above. Where H₂ ^(k) is thelargest size Hadamard matrix used in the hybrid method, the signals onthe bus will be at most √{square root over (2 ^(k))} times larger thanthe maximum signals entering the transformer 110 (FIG. 1). By choosing kappropriately, this factor can be made as smaller, though at thedetriment of the pin-efficiency. For example, if the number of incomingwires into transformer 110 is 15, it is possible to use 5 copies of thetransformer with Hadamard matrix H₄ to obtain a signal amplificationratio of √{square root over (4)}=2 and a pin-efficiency of 0.75.

However, another method can be used to simultaneously keep thepin-efficiency 15/16 of the transformer with Hadamard matrix H₁₆ and asignal amplification ratio of 2. To achieve this, a set subset S of 16dimensional vectors is constructed for which the entries are +1 and −1,and for which the maximum absolute value of any of the entries of themultiplication of H₁₆ with any of the elements of this set is at most 2.Such a subset exists, and the largest such subset has 43232 elements. Bypicking 2¹⁵=32768 vectors among these, and mapping each of the 32768constellations of the incoming 15 signals uniquely to one of thesevectors, the pin-efficiency of 15/16 is maintained, and the signalamplification ratio is reduced to 2.

Another example is the transformer with Hadamard matrix H₃₂. Thepin-efficiency of this transformer is 31/32 which is about 97% and itsworst case signal amplification ratio is 32 which is about 5.66.However, by computing the possible produces of H₃₂ with 32-dimensionalvectors with entries +1 or −1, it is possible to exhibit subsets S₁, S₂,S₃, S₄, S₅, S₆, S₇, of sizes 2⁵, 2 ⁹, 2 ¹², 2 ²⁴, 2 ²⁹, 2 ³⁰, 2 ³¹ ofthe set of all 32-dimensional vectors with entries +1 or −1 such thatthe approximate worst case signal amplification ratio of these subsetsis given by the following table:

S₁ S₂ S₃ S₄ S₅ S₆ S₇ 0.3536 0.7071 1.061 1.4142 1.7678 2.1213 2.4749

For each of these subsets, by mapping constellations of incoming signalsets (of size 5, 9, 12, 24, 29, 30 and 31, respectively) uniquely to theelements of these subsets, a differential vector signaling procedure isobtained that has the following approximate pin-efficiency and signalamplification ratio:

S₁ S₂ S₃ S₄ S₅ S₆ S₇ Pin- 0.15625 0.28125 0.375 0.75 0.90625 0.93750.96875 efficiency Ampli- 0.3536 0.7071 1.061 1.4142 1.7678 2.12132.4749 fication ratio

Other Orthogonal and Unitary Matrices

Some of the above examples in accordance with at least one embodiment ofthe invention have been described with respect to Hadamard matrices.However, each embodiment of the invention is not so limited. As isappreciated by those of skill in the art, a Hadamard matrix can bereplaced by any suitable orthogonal matrix. Examples of suitableorthogonal matrices in accordance with at least one embodiment of theinvention include non-simple orthogonal matrices which transform avector with similar entries into a vector that has zeros in asignificant proportion (e.g., a majority) of its positions. For thepurposes of this description, simple orthogonal matrices include squarematrices of size 1 (i.e., 1×1 matrices) and their equivalents, theHadamard matrix of size 2 and its equivalents, and direct sums (in thesense of group theory) of the Hadamard matrix of size 2 and theirequivalents. The signal information may be encoded in the nonzeropositions of the resultant vectors. If t is the maximum number ofnonzero positions of such a vector, then the pin-efficiency of thecorresponding orthogonal differential vector signaling scheme can bem/(m+t).

Where the incoming signals can be interpreted as complex numbers, adifferent type of matrix can be used to obtain similar advantages asthose obtained by orthogonal matrices in accordance with at least oneembodiment of the invention. Such matrices include unitary matrices,which, for the purposes of this description, are matrices for which therows are normalized to have Euclidean length one, and for which the rowsare orthogonal with respect to the Hermitian scalar product. As can beappreciated by those of skill in the art, some such matrices may provideadvantages similar to those of Hadamard matrices in accordance with atleast one embodiment of the present invention. One example of such amatrix is

$\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\i & {- i}\end{bmatrix}$

where, as is conventional, i is the imaginary unit. Other examples couldinclude higher Kronecker powers of this matrix. For example, the secondKronecker power of this matrix is

$\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\i & {- i} & i & {- i} \\i & i & {- i} & {- i} \\1 & {- 1} & 1 & 1\end{bmatrix}$

Other types of unitary matrices can be envisioned which have propertiessimilar to those of Hadamard matrices. For example, a class of suchmatrices can comprise all matrices of the form

$H\begin{bmatrix}a_{1} & 0 & \ldots & 0 & 0 \\0 & a_{2} & \ldots & 0 & 0 \\\vdots & \vdots & \ddots & \vdots & \vdots \\0 & 0 & \ldots & a_{n - 1} & 0 \\0 & 0 & \ldots & 0 & a_{n}\end{bmatrix}$

wherein a₁, . . . , a_(n) are complex numbers of magnitude 1 and H is aHadamard matrix. It is also possible to use such matrices in which a₁, .. . , a_(n) are not of magnitude one, but of some other magnitude (e.g.,1+c, where the absolute value |ε| is at least an order of magnitude lessthan one). In this case the resulting matrix is not unitary, but may beclose to a unitary matrix (i.e., a “near-unitary matrix”) and may beused in accordance with at least one embodiment of the presentinvention.

For the purposes of this description, orthogonal matrices maydifferentiate from unitary matrices in that orthogonal matrices have allreal entries, whereas unitary matrices have at least one complex entry.Accordingly, simple unitary matrices include equivalents of simpleorthogonal matrices having at least one complex entry. Furthermore, forthe purposes of this description, near-orthogonal matrices are theequivalents of near-unitary matrices having all real entries, forexample, matrices obtained by multiplying a Hadamard matrix with adiagonal matrix (from the left or from the right) in which the diagonalentries have absolute values that are not too large or too small. In atleast one embodiment of the invention, non-simple orthogonal matricesinclude near-orthogonal matrices. In at least one embodiment of theinvention, non-simple unitary matrices include near-unitary matrices.

Other Modes of Operation

Orthogonal differential vector signaling can be used in many differentways in accordance with embodiments of the present invention. Forexample, in some embodiments of the present invention, it may bedesirable to sacrifice pin-efficiency for higher noise resilience. Forexample, where there are 32 incoming bits, a bus of size 64 can be usedto transmit these bits. The values of these bits can be calculated bypadding the 32 incoming values with 32 zeroes or other known values, andtransforming the 64 values obtained this way using a Hadamard matrix ofSylvester type. The resulting 64 wires have a higher resilience to noisethan the 64 wires obtained from the original 32 signals using pairs ofdifferential signals. For example, if one of these pairs is subjected toa high amount of noise, then the information in that pair is entirelylost. However, by zero-padding the 32 signals with zeroes and obtaining64 signals transmitted on wires, concentrated noise on two neighboringwires is, after the reverse Hadamard transformation, spread to a muchsmaller amount of noise (almost 32 times less) on every one of the 64signals. Using conventional detection techniques, this noise can becanceled if it is not catastrophically large. The padding operation canalso be used in conjunction with hybrid methods.

In another mode of operation in accordance with embodiments of theinvention, the physical space reserved for signal paths can be the sameas that of a conventional differential signaling method. However, giventhe higher pin-efficiency of methods in accordance with embodiments ofthe invention, the signal paths (e.g., wires) can be spread furtherapart, leading to smaller interference between neighboring signal paths,and hence reducing crosstalk noise. The method can be used to reducephysical signal path spacing and crosstalk noise at the same time: forexample, by physically spreading the signal paths by a factor of√{square root over (2)} times a basic distance, the crosstalk noise maybe reduced by a factor of almost 2, and the total width of the bus ascompared to normal differential signaling may be reduced by anotherfactor of √{square root over (2)}.

Some Application Spaces and Brief Descriptions

The teachings of this disclosure are applicable in a variety ofsituations in which information such as digital information is to betransmitted in a tangible and/or physical form from a source to adestination. For example, where the transmission takes place withrespect to a communications bus capable of physically carrying signalspertaining to the information. Below a partial list of such applicationsare discussed. This list is for illustrative purposes only, and is notexhaustive.

DSL Lines

One application is DSL communications where Discrete Multitone (DMT)modulated signals or Quadrature Amplitude Modulation (QAM) modulatedsignals are sent differentially over a twisted copper pair from thecentral office to the customer side modem. FIG. 16 illustrates thisscenario. The central office 1610 is connected to a DSL modem 1630 at anend user location 1620 (e.g., a consumer home) by a twisted pair copperwire 1650. As is often the case, there is an unused twisted pair 1640.

The DSL communications may be enhanced by increasing the total bit rateas follows. In this case, the bus 120 (FIG. 1) is made up of themultiple twisted pairs (1640, 1650 with reference to FIG. 16). Anillustration of the signaling technique applied is given in FIG. 17. Atthe central office 1610, the output of several modems 1730, whichtypically originate from a DSL Access Multiplexer (DSLAM), are fed tothe transformer 110. The output of the transformer 110 is fed to the bus120 and a detransformer 130 constructs the original signals for themodems 1740 at the consumer side.

In this case, the transformer 110 and detransformer 130 could beimplemented with analog electronic circuitry such that existing DSLtechniques and/or unmodified conventional DSL equipment can utilize theinvention. Furthermore, the technique can be used together with linkaggregation techniques to create one virtual link for the end user 1620.This would allow operators to integrate the technique into theirnetworks and provide a link with a higher bit rate to the end users.

To give a specific example, in most countries operators have two pairsconnecting the central office to the end user. In such a scenario, anembodiment of the present invention would choose a bus including 4 wireson which 3 DSL modem signals can be multiplexed. This could potentiallytriple the available bandwidth for the end user. In addition, thetechnique disclosed in this application can be combined withmultiple-input multiple-output (MIMO) techniques to cancel crosstalknoise and triple the data rate on the link. Furthermore, in accordancewith at least one embodiment of the invention, each signal may be spreadon all wires of the bus and making it more resilient against impulsenoise that occurs on one of the lines.

Chip-to-Chip Communication

Today, many electronic devices such as TVs, mobile phones, cameras andpersonal computers have fast processors. These processors communicatewith peripheral devices such as memory by means of communication buses.Especially for high-speed memory access, increasing bandwidth is anissue. Problems in increasing bandwidth are mainly caused by an increaseof noise and interference due to the high signaling speeds.

In chip-to-chip communications there are several noise sources. Some ofthe most important ones are noise introduced by signal path transmittersand receivers, common-mode noise and interference, simultaneousswitching output noise and reference voltage noise.

Methods for chip-to-chip communications typically use eithersingle-ended signaling, or conventional differential signaling.Orthogonal differential vector signaling in accordance with at least oneembodiment of the invention has at least some of the advantages ofconventional differential signaling with a much smaller expansion of thebus width (e.g., due to its relatively high pin-efficiency). One examplewhere large gains can be obtained is CPU-to-CPU and CPU-to-memorycommunications in multi-core processors. For this application bandwidthmay be significant. Furthermore, wide data busses can cause problemswith respect to routing. Systems and methods in accordance with at leastone embodiment of the invention may enable at least some of theadvantages of conventional differential signaling while requiringsmaller bus widths.

Optical Fiber Communication

In optical fiber communications an electrical signal carryinginformation is converted into light and transmitted on an optical fiber.Intensity modulation is the most common form of modulation used.Intensity modulation can be compared with single-ended signaling in thesense that a reference to which one compares the intensity of the lightat the other end of the fiber has to be available. In applications,replicating the same intensity on both ends of the communication pathmay be difficult and costly to attain. This problem can be solved byusing differential signaling. For high throughput optical fiber links,multiple fibers can be used in parallel. In accordance with at least oneembodiment of the invention, it is possible to transmit n-1 informationcarrying signals on n optical fibers. The bus 120 would include the nfibers. Methods in accordance with at least one embodiment of theinvention need not require a reference or conventional differentialencoding. As will be apparent to one of skill in the art, this can leadto increased data rates and better performance with respect to noise.

Device-to-Device Communications

Devices such as mobile phones, TVs, computers, laptops, and digitalcameras sometimes support interfaces for inter-device communications.Examples of communication standards are DVI, HDMI, USB, and FireWire. Inall these applications the bus may include wires where mostlydifferential signaling is used to cope with common-mode interference. Inaccordance with at least one embodiment of the invention, the bus 120(FIG. 1) may include and/or be included by the connection between twosuch devices. With the orthogonal differential vector signaling method,the number of wires in the cable can be substantially reduced withoutgiving up on a common-mode noise protection. In accordance with at leastanother embodiment of the invention, the number of wires in the cablemay be kept the same while substantially increasing the throughput ofthe cables.

Other instances of device-to-device communication include but are notlimited to the communication between hard disks and a computer mainboard, the communication between expansion cards and computers andcommunication between networking cards over Unshielded Twisted Pair(UTP) cables. These and other suitable communication scenarios canbenefit in accordance with at least one embodiment of the invention.

Example Steps

For clarity, FIG. 18 depicts example steps that may be performed inaccordance with at least one embodiment of the invention. At step 1802,an unbalanced signal set may be received. For example, the unbalancedsignal set may be received by the transformer 110 (FIG. 1). At step1804, a balancing transformation may be applied. For example, thebalancer 210 (FIG. 2) may apply the balancing transformation to theunbalanced signal set received at step 1802 as at least a part of aprocess of forming a balanced signal set. At step 1806, a balancedsignal set may be provided. For example, the balancer 210 may providethe balanced signal set formed at least in part at step 1804 to theencoder 220. The steps 1802, 1804 and 1806 are enclosed in a dash line1808 to indicate that they may be part of a set of signal balancingsteps 1808.

At step 1810, an input signal set may be received. For example, theencoder 220 (FIG. 2) may receive the input signal set. At step 1812, anon-simple orthogonal transform may be applied. For example, the encoder220 may apply the non-simple orthogonal transform to the input signalset received at step 1810 as at least a part of a process of forming atransmission signal set. At step 1814, a transmission signal set may beprovided. For example, the transformer 110 (FIG. 1) may provide thetransmission signal set formed at least in part at step 1812 to the bus120 for transmission. The steps 1810, 1812 and 1814 are enclosed in adash line 1816 to indicate that they may be part of a set of signalencoding steps 1816.

At step 1818, a signal set may be transmitted over a data bus. Forexample, the transmission signal set provided to the bus 120 (FIG. 1) atstep 1814 may be transmitted from a first portion of the bus 120 to asecond portion of the bus 120. The first and second portions of the bus120 may correspond to physically distinct and/or disjoint portions ofthe bus 120. The bus 120 may include multiple signal paths, and the bus120 may transmit each signal in the transmission signal set over asingle one of the multiple signal paths.

At step 1820, a transmitted signal set may be received. For example, thedetransformer 130 (FIG. 1) may receive the transmitted signal set fromthe bus 120. The transmitted signal set may correspond to thetransmission signal set provided at step 1814 as corrupted during itsjourney over the bus 120, for example, as corrupted by noise. At step1822, a non-simple orthogonal transform may be applied. For example, thedecoder 720 (FIG. 7) may apply the non-simple orthogonal transform tothe transmitted signal set received at step 1820 as at least a part of aprocess of forming an output signal set. The non-simple orthogonaltransform applied at step 1822 may correspond to the non-simpleorthogonal transform applied at step 1812. For example, the non-simpleorthogonal transform applied at step 1822 may be the same, similarand/or complementary to the non-simple orthogonal transform applied atstep 1812. At step 1824, an output signal set may be provided. Forexample, the detransformer 130 may provide the output signal set formedat least in part at step 1822 to the communication device 104. The steps1820, 1822 and 1824 are enclosed in a dash line 1826 to indicate thatthey may be part of a set of signal decoding steps 1826.

Preferred embodiments are described herein, including the best modeknown to the inventors. Further embodiments can be envisioned by one ofordinary skill in the art after reading this disclosure. In otherembodiments, combinations or sub-combinations of the above disclosedinvention can be advantageously made. The example arrangements ofcomponents are shown for purposes of illustration and it should beunderstood that combinations, additions, re-arrangements, and the likeare contemplated in alternative embodiments of the present invention.Thus, while the invention has been described with respect to exemplaryembodiments, one skilled in the art will recognize that numerousmodifications are possible.

For example, the processes described herein may be implemented usinganalog or digital hardware components, software components, and/or anycombination thereof. The specification and drawings are, accordingly, tobe regarded in an illustrative rather than a restrictive sense. It will,however, be evident that various modifications and changes may be madethereunto without departing from the broader spirit and scope of theinvention as set forth in the claims and that the invention is intendedto cover all modifications and equivalents within the scope of thefollowing claims.

The use of the terms “a” and “an” and “the” and similar referents in thecontext of describing embodiments (especially in the context of thefollowing claims) are to be construed to cover both the singular and theplural, unless otherwise indicated herein or clearly contradicted bycontext. The terms “comprising,” “having,” “including,” and “containing”are to be construed as open-ended terms (i.e., meaning “including, butnot limited to,”) unless otherwise noted. The term “connected” is to beconstrued as partly or wholly contained within, attached to, or joinedtogether, even if there is something intervening. Recitation of rangesof values herein are merely intended to serve as a shorthand method ofreferring individually to each separate value falling within the range,unless otherwise indicated herein, and each separate value isincorporated into the specification as if it were individually recitedherein. All methods described herein can be performed in any suitableorder unless otherwise indicated herein or otherwise clearlycontradicted by context. The use of any and all examples, or exemplarylanguage (e.g., “such as”) provided herein, is intended merely to betterilluminate embodiments and does not pose a limitation on the scopeunless otherwise claimed. No language in the specification should beconstrued as indicating any non-claimed element as essential to thepractice of at least one embodiment.

All references, including publications, patent applications, andpatents, cited herein are hereby incorporated by reference to the sameextent as if each reference were individually and specifically indicatedto be incorporated by reference and were set forth in its entiretyherein.

What is claimed is:
 1. A method comprising: obtaining an input vectorcomprising a plurality of multilevel signals, each multilevel signalhaving a signal value selected from a set of more than two signalvalues; generating a set of output signals from the input vector ofmultilevel signals, each output signal generated on a respective wire ofa multi-wire bus responsive to a respective additive computation of theplurality of multilevel signals, each respective additive computationdetermined according to a respective row of a set of mutually orthogonalrows of an orthogonal matrix; and transmitting the set of output signalsover the multi-wire bus.
 2. The method of claim 1, wherein eachmultilevel signal of the plurality of multilevel signals is representedas a multi-bit value.
 3. The method of claim 1, wherein the plurality ofmultilevel signals comprises N−1 signals, and wherein the set of outputsignals comprises N output signals, wherein N is an integer power of twogreater than
 2. 4. The method of claim 1, wherein the orthogonal matrixis a Hadamard matrix.
 5. The method of claim 4, wherein one of themulti-level signals is a constant value associated with a column of theorthogonal matrix consisting entirely of ones.
 6. The method of claim 5,wherein the constant value is a non-zero value ‘V’, and the column ofthe orthogonal matrix consisting entirely of ones induces an offset ‘V’to the output signals on the multi-wire bus.
 7. The method of claim 5,wherein the constant value is zero to eliminate any effect of the columnof the orthogonal matrix consisting entirely of ones on the multi-wirebus.
 8. The method of claim 1, wherein each respective additivecomputation is performed by a series of additions and subtractions asdetermined by ‘+1’ and ‘−1’ entries, respectively, in the respective rowof the orthogonal matrix.
 9. The method of claim 1, further comprisingforming a second set of signals using a decoder, each respective signalof the second set based on a transformation of the set of signals with arespective row of the set of mutually orthogonal rows of the orthogonalmatrix, wherein each respective signal in the second set of signals hasan analog value selected from a respective set of more than two values;and reproducing original information from the second set of signals. 10.The method of claim 9, wherein reproducing the original information fromthe second set of signals comprises generating a multi-bit value foreach signal of the second set of signals.
 11. An apparatus comprising: astorage medium configured to provide an input vector to an encoder, theinput vector comprising a plurality of multilevel signals, eachmultilevel signal having a signal value selected from a set of more thantwo signal values; the encoder configured to generate a set of outputsignals from the input vector of multilevel signals, each output signalgenerated on a respective wire of a multi-wire bus responsive to arespective additive computation of the plurality of multilevel signals,each respective additive computation determined according to arespective row of a set of mutually orthogonal rows of an orthogonalmatrix; and a set of signal path drivers configured to transmit the setof output signals over the multi-wire bus.
 12. The apparatus of claim11, wherein the storage medium is configured to store each multilevelsignal of the plurality of multilevel signals as a multi-bit value. 13.The apparatus of claim 11, wherein the plurality of multilevel signalscomprises N−1 signals, and wherein the set of output signals comprises Noutput signals, wherein N is an integer power of two greater than
 2. 14.The apparatus of claim 11, wherein the orthogonal matrix is a Hadamardmatrix.
 15. The apparatus of claim 14, wherein one of the multi-levelsignals is a constant value associated with a column of the orthogonalmatrix consisting entirely of ones.
 16. The apparatus of claim 15,wherein the constant value is a non-zero value ‘V’, and the column ofthe orthogonal matrix consisting entirely of ones induces an offset ‘V’to the output signals on the multi-wire bus.
 17. The apparatus of claim15, wherein the constant value is zero to eliminate any effect of thecolumn of the orthogonal matrix consisting entirely of ones on themulti-wire bus.
 18. The apparatus of claim 11, wherein the encoder isconfigured to generate each respective additive computation by forming aseries of additions and subtractions as determined by ‘+1’ and ‘−1’entries, respectively, in the respective row of the orthogonal matrix.19. The apparatus of claim 11, further comprising a decoder configuredto receive the set of output signals, and to responsively form a secondset of signals, each respective signal of the second set based on atransformation of the set of output signals with a respective row of theset of mutually orthogonal rows of the orthogonal matrix, wherein eachrespective signal in the second set of signals has an analog valueselected from a respective set of more than two values; and a detectorconfigured to reproduce original information from the second set ofsignals.
 20. The apparatus of claim 19, wherein the detector isconfigured to generate a multi-bit value for each signal of the secondset of signals to reproduce the original information.